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Exercises $67-78$ give parametric equations and parameter intervals for the motion of a particle in the $x y$ -plane. Identify the particle's path by finding a...

Question

Exercises $67-78$ give parametric equations and parameter intervals for the motion of a particle in the $x y$ -plane. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. The graphs will vary with the equation used.) Indicate the portion of the graph traced by the particle and the direction of motion. $$ x=\sec ^{2} t-1, \quad y=\tan t, \quad-\pi / 2< t <\pi / 2 $$

Exercises $67-78$ give parametric equations and parameter intervals for the motion of a particle in the $x y$ -plane. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. The graphs will vary with the equation used.) Indicate the portion of the graph traced by the particle and the direction of motion. $$ x=\sec ^{2} t-1, \quad y=\tan t, \quad-\pi / 2< t <\pi / 2 $$



Answers

Exercises $67-78$ give parametric equations and parameter intervals for the motion of a particle in the $x y$ -plane. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. The graphs will vary with the equation used.) Indicate the portion of the graph traced by the particle and the direction of motion.
$$
x=\sec ^{2} t-1, \quad y=\tan t, \quad-\pi / 2< t <\pi / 2
$$


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